A Leland Model for Delta Hedging in Central Risk Books

34 Pages Posted: 28 Mar 2022

See all articles by Johannes Muhle-Karbe

Johannes Muhle-Karbe

Imperial College London - Department of Mathematics

Zexin Wang

Imperial College London - Department of Mathematics

Kevin Webster

Columbia University

Date Written: March 4, 2022

Abstract

Using a tractable extension of the Leland (1985) model, we study how a delta-hedging strategy can realistically be implemented using market and limit orders in a centralized, automated market-making desk that integrates trading and liquidity provision for both options and their underlyings. In the continuous-time limit, the optimal limit-order exposure can be computed explicitly by a pointwise maximization. It is determined by the relative magnitudes of adverse selection, bid-ask spreads, and volatilities. The corresponding option price (from which the option can be replicated using market and limit orders) is characterized via a nonlinear PDE.

Our results highlight the benefit of tactical liquidity provision for contrarian trading strategies, even for a trading desk that is not a competitive market maker. More generally, the paper also showcases how reduced-form models are competitive with "brute force" numerical approaches to market microstructure. Both the estimation of microstructure parameters, and the simulation of the optimal trading strategy are made concrete and reconciled with real-life high frequency data.

Keywords: Market microstructure, market making, central risk book, limit orders, adverse selection

JEL Classification: C61, G13, G14

Suggested Citation

Muhle-Karbe, Johannes and Wang, Zexin and Webster, Kevin, A Leland Model for Delta Hedging in Central Risk Books (March 4, 2022). Available at SSRN: https://ssrn.com/abstract=4049864 or http://dx.doi.org/10.2139/ssrn.4049864

Johannes Muhle-Karbe (Contact Author)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
LONDON, SW7 1NE
United Kingdom

HOME PAGE: http://www.ma.imperial.ac.uk/~jmuhleka/

Zexin Wang

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
LONDON, SW7 2AZ
United Kingdom

Kevin Webster

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

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